报告人及报告简介:
报告人: 徐岩 (中国科学技术大学)
报告题目: A kernel compensation mimetic finite difference scheme for eigenvalue problem
报告摘要: We propose a kernel compensation type mimetic finite difference (MFD) scheme aimed at solving the grad-div eigenvalue problem. This method utilizes a curl-curl type compensation operator along with carefully selected boundary conditions to effectively manage the infinite-dimensional kernel of the grad-div operator. To ensure high accuracy, we apply stencil-based mimetic finite difference operators to discretize the grad-div operator under Dirichlet boundary conditions. This results in a numerical scheme characterized by a sparse stiff matrix with a narrow bandwidth while achieving high-order accuracy. We construct the compensation operator with a proper boundary condition that is orthogonal with the discrete grad-div operator. Generalized identify method for spurious eigenvalues are presented. The resulting scheme offers several advantages, including high-order accuracy, enhanced computational efficiency with reduced memory usage, and excellent scalability for parallel computation. Numerical tests demonstrate that our approach not only converges at the expected rates but also performs satisfactorily in terms of speed.
报告人简介: 徐岩，中国科学技术大学数学科学学院教授、博导，教育部国家重大人才工程项目特聘教授, 国家自然科学基金优秀青年基金、教育部新世纪优秀人才计划、中国数学会计算数学分会第二届“青年创新奖”获得者。主要研究领域为高精度数值计算方法。担任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、计算物理等杂志的编委。
报告人: Matthias Schlottbom (University of Twente)
报告题目: Residual minimization-based acceleration of iterative schemes for radiative transfer
报告摘要: The numerical solution of the radiative transfer equation requires the solution of very large linear systems. In the past decades a vast amount of iterative schemes has been devised to solve this task. To accelerate convergence of such iterative methods, preconditioners have been developed that solve a diffusion problem, which can be well motivated using arguments from asymptotic analysis. It has been observed that special care needs to be taken in the discretization of such diffusion problems to preserve convergence, leading to so-called consistent schemes. In this talk, we take a slightly different point of view and use preconditioners that are based on residual minimization over suitable subspaces. We prove convergence of the resulting iteration using Hilbert space norms, which allows us to obtain algorithms that converge robustly with respect to finite dimensional realizations via Galerkin projections. We investigate in particular the behavior of the iterative scheme for discontinuous Galerkin discretizations in the angular variable in combination with subspaces that are derived from related diffusion problems. The performance of the resulting schemes is investigated in numerical examples for highly anisotropic scattering problems with heterogeneous parameters.
报告人简介: Matthias Schlottbom (MS) received his PhD (2011) from RWTH Aachen with the highest honors for his work on forward and inverse problems in optical tomography, for which he received the Borchers medallion. He did PostDocs at TU Munich (2011-2012), TU Darmstadt (2012-2014), and WWU Münster (2014-2016). In 2016, he joined the University of Twente where he chairs the Mathematics of Computational Science group. MS is a member of the board of the Dutch-Flemish Scientific Computing Society. Since 2025, he is also an international visiting professor at the University of Science and Technology of China (USTC).
His research focuses on numerical analysis and inverse problems for partial differential equations, with applications in radiative transfer problems. He co-authored more than 40 articles that appeared in various journals, such as SIAM (mathematical analysis, scientific computing, numerical analysis), foundations of computational mathematics, journal of differential equations, or inverse problems.
报告人: 夏银华 (中国科学技术大学)
报告题目: A globally divergence-free and positivity-preserving discontinuous Galerkin method for ideal MHD equations with the jump filter
报告摘要: In this talk, we introduce a high-order discontinuous Galerkin (DG) scheme that simultaneously ensures positivity-preserving (PP) properties and maintains the globally divergence-free (GDF) constraint for the ideal magnetohydrodynamics (MHD) equations. Achieving both conditions remains quite challenging in MHD simulations when the PP and GDF reconstructions (theoretically linked) are treated as independent post-processing operations. To overcome this difficulty, we propose the pointwise pressure-preserving correction method, which is easy to implement and highly effective. Specifically, based on the equation of state, we recompute the total energy values at integration nodes using PP hydrodynamic variables and the GDF magnetic field. As long as the GDF magnetic field is highly accurate, the total energy obtained through this correction technique can also maintain high accuracy. The key technique for proving the PP property of the GDF-DG scheme involves the convex decomposition of cell averages. With the geometric quasilinearization framework introduced by Wu et al., our GDF-DG scheme can be theoretically shown to satisfy the PP property. To suppress spurious oscillations, we adopt the jump filter for ideal MHD equations, as a sequel to our recent work. This filter operates locally based on jump information at cell interfaces, and preserves key attributes of the DG method, such as conservation, L2 stability, and high-order accuracy. Moreover, it boasts an impressively low computational cost, given that no local characteristic decomposition is required and all computations are confined to the physical space. The jump filter is applied after each Runge-Kutta stage without altering the DG spatial discretization and maintains both the GDF and PP properties of the scheme. Numerical simulations demonstrate the accuracy, effectiveness, and robustness of the proposed PP-GDF-DG schemes with the jump filter.
报告人简介: 夏银华，中国科学技术大学数学科学学院，教授，博士生导师，安徽省领军人才特聘教授。中国科学技术大学数学系获得博士学位，曾先后到美国布朗大学、香港大学、德国维堡大学等从事博士后研究和访问工作。主要从事高精度数值方法和大规模科学计算的研究，应用于计算流体、天体物理、相场问题、交通流等方面的数值模拟。相关工作发表在包括Math. Comp., J. Comput. Phys., J. Sci. Comput., SIAM J. Num. Anal., SIAM J. Sci. Comput.等杂志。主持国家自然科学基金、教育部、安徽省杰青项目等多项科学基金项目的研究。
主办单位：扬州大学数学学院
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